1. Expanding and Simplifying Algebraic Expressions
2(x + 1) + 3(x + 3)
= 2x x + 9
= 5x + 11
x + x
= 2x
2x - 5x
= -3x

2. (x - 1)(4)
Four groups
of (x - 1)

3. (x - 1)(4)
This is
a zero
model.

4. How can you use algebra tiles to show that
(x - 1)(4) = 2 + 4x
The simplified expression is
2 + 4x or
4x + 2.
How can you use algebra tiles to show that
2 + 4x is the same as 4x + 2 ?

5. Simplify:
2x x - 5
x - 2x
3 (x - 1)
-2 (x + 2)

6. Simplify:
x x - 5

7. Simplify:
1. 2x x - 5
= 6x - 2
zero

8. Simplify:
2. x - 2x

9. Simplify:
= -x - 6
2. x - 2x
zero

10. How could you get this answer without using algebra tiles?
Simplify:
(x - 1)
= 3x - 3
How could you get this answer without using algebra tiles?

11. Simplify:
(x - 2)
Step 1
2 (x - 2)
Step 2
The opposite

12. How could you get this answer without using algebra tiles?
Simplify:
(x - 2)
= -2x + 4
2 (x - 2)
-2 (x - 2)
How could you get this answer without using algebra tiles?

13. Steps without algebra tiles
-2 (x - 2) + 3 (2x + 1)
= -2x x + 3
= 4x + 7
How could you check your answer
to see if it is equivalent to the original expression?